Import Question JSON

Current Question (ID: 16460)

Question:

$\text{A point charge } q \text{ is placed at the center of the open face of a hemispherical}$ $\text{surface as shown in the figure. The flux linked with the surface is:}$

Options:

1. $\text{zero}$
2. $\frac{q}{2\varepsilon_0}$
3. $\frac{q}{\varepsilon_0}$
4. $q\pi r^2$

Solution:

$\text{Hint: } \phi_{\text{sphere}} = \frac{q}{\varepsilon_0}$ $\text{Step: Find the flux linked with the surface.}$ $\text{The flux of the electric field due to a charge placed at the center of the}$ $\text{sphere is given by;}$ $\phi_{\text{sphere}} = \frac{q}{\varepsilon_0}$ $\text{Hemispherical flux: Since a hemisphere is half of a full sphere, the flux}$ $\text{through the curved surface of the hemisphere is half of the total flux.}$ $\text{Hence, the flux of the electric field due to a charge placed at the center of}$ $\text{the hemisphere is given by;}$ $\phi_{\text{hemisphere}} = \frac{1}{2} \phi_{\text{sphere}} = \frac{1}{2} \frac{q}{\varepsilon_0}$ $\text{Hence, option (2) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}